You can take flood icing as thick as you want, as long as it spreads smoothly.
As for dehydrators, there is an entire post on this site about which ones are the best to buy for cookies (pros and cons of various models). Check it out; it explains a lot: http://cookieconnection.juliau...ator-recommendations
Without being there to see what you did, it's very hard to say why one mottled and the other did not . . . there are many variables (ambient conditions being just one), so even the time of day could have influenced the outcome. Or perhaps the cookies that you dried in the oven got too hot and some of the oils leached into the icing? Or perhaps the icing consistencies were a little different? Or maybe you dried one longer than another?? You see my point.
But the quick answer is: the faster an icing sets, the less likely colors are to bleed or mottle. And the thicker the icing to start, the faster it sets (as there is less water in it to evaporate).